Empirical Bayesian Kriging and EBK Regression Prediction – Robust Kriging as Geoprocessing Tools Eric Krause

What is interpolation? Predict values at unknown locations using values at measured locations Many interpolation methods: kriging, IDW, LPI, etc

Semivariogram Modeling

Empirical Bayesian Kriging Advantages Requires minimal interactive modeling, spatial relationships are modeled automatically Usually more accurate, especially for small or nonstationary datasets Uses local models to capture small scale effects Doesn’t assume one model fits the entire data Standard errors of prediction are more accurate than other kriging methods Disadvantages Processing is slower than other kriging methods Limited customization

How does EBK work? Divide the data into subsets of a given size Controlled by “Subset Size” parameter Subsets can overlap, controlled by “Overlap Factor” For each subset, estimate the semivariogram Simulate data at input point locations and estimate new semivariogram from the simulated data Repeat step 3 many times. This results in a distribution of semivariograms Controlled by “Number of Simulations” Mix the local surfaces together to get the final surface.

EBK Regression Prediction New tool available in ArcGIS Pro 1.2 Allows you to use explanatory variable rasters to improve predictions Automatically extracts useful information from explanatory variables Uses Principle Components to handle multicollinearity

Transformations Two available transformations Empirical – Fits a smooth distribution to the data, then transforms to normal distribution. Useful for data that is not bell-shaped Log Empirical – Takes logarithm of data before performing Empirical transformation. Useful for data that cannot be negative (eg, rainfall)

Data in Geographic Coordinate Systems Euclidean distance for geographic coordinates is very inaccurate, particularly far from the equator In ArcGIS 10.3, EBK uses chordal distances Chordal distance is the 3D straight-line distance between points on a spheroid Accurate approximation to geodesic distance up to 30 degrees

Empirical Bayesian Kriging and EBK Regression Prediction Demo Empirical Bayesian Kriging and EBK Regression Prediction Eric Krause Eric Krause